4.7,4.8, 5.1

4.7,4.8, 5.1 - given B P(A intersection B = P(B X P(A|B...

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Lecture 6: 4.7 Bayes Rule, 4.8 Counting Rules, 5.1 Random Variables Addition Rules Special Addition Rule: For mutually exclusive events only. P(A U B) = P(A) + P(B) Complementation Rule: Sometimes it’s easier to find the probability of an event not occurring, than finding the probability of an event occurring. P (E occurring) = 1- P(E not occurring) General Addition Rule: P (A U B)= P(A) + P(B) – P(A intersection B) Multiplication Rules Special Multiplication Rule: For independent events only. Their joint probability = the product of their marginal probabilities. P(A intersection B) = P(A) X P(B) General Multiplication Rule: Their joint probability = The marginal probability of B and the conditional probability A
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Unformatted text preview: given B P (A intersection B) = P(B) X P(A|B) Rule of Total Probability Exhaustive events are events in which one or more of them must occur. Ex: A politician selected is either Republican, Democrat or Independent. One of them must occur. A collection of events is a partition of the sample space if the events are mutually exclusive and exhaustive. If they are both, then exactly one of them must occur because the events must occur (if they’re exhaustive) and at most one of the events can occur (if the events are mutually exclusive). The Rule of Total Probability is the denominator of Bayes Rule and it applies to mutually exclusive and exhaustive events....
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